The Oxford English Dictionary gives a 'clasper' as "one who puts clasps on old books", but this appears to post date the origins of the name. Another theory was that the name derived from 'clapper' when the double 'p' was written in Old English.
It has also been suggested that CLASPER is a Hanoverien name. But, Hanovarien immigration started after the origin of the name CLASPER in the North-East of England where immigrants from Europe settled.
But the most probable explanation is that the name is quite simply a metonymic surname meaning exactly what is says "a maker or dealer in clasps". These were an essential part of Medieval clothing for both men and women. Ornamental clasps and also workaday ones were manufactured by claspers.